Nuclear Physics Challenge #2 — Decay Chains

Balancing a
decay equation.

Nuclear Physics Hard

Problem

A nucleus of uranium-238 \( (Z = 92) \) undergoes two alpha decays followed by two beta-minus decays. Determine the atomic number \( Z \) of the resulting nucleus.

Start\( ^{238}_{92}\mathrm{U} \)
Alpha decay\( A{-}4,\ Z{-}2 \)
Beta-minus decay\( A\ \mathrm{same},\ Z{+}1 \)
Answer asatomic number Z

Track A and Z separately — only one of them survives the betas unchanged.

Hint: each alpha removes a helium nucleus \( (A{-}4,\ Z{-}2) \); each beta-minus turns a neutron into a proton \( (Z{+}1,\ A\ \mathrm{unchanged}) \). Apply them one at a time.

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Balancing adecay equation.

Problem